What is the general solution for 4sin(3x)=7cos(3x) ?

The general solution for 4sin(3x)=7cos(3x) is x=(1.05165…)/3+(pin)/3

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4sin(3x)=7cos(3x)

4 sin (3 x) = 7 cos (3 x)

x = \frac{1.05165 \dots}{3} + \frac{πn}{3}

Degrees

x = 20.08503 \dots^{\circ} + 6 0^{\circ} n

Solution steps

4 sin (3 x) = 7 cos (3 x)

Rewrite using trig identities

4 sin (3 x) = 7 cos (3 x)

Divide both sides by

cos (3 x), cos (3 x) \neq = 0

\frac{4 sin ( 3 x )}{cos ( 3 x )} = \frac{7 cos ( 3 x )}{cos ( 3 x )}

Simplify

\frac{4 sin ( 3 x )}{cos ( 3 x )} = 7

Use the basic trigonometric identity:

\frac{sin ( x )}{cos ( x )} = tan (x)

4 tan (3 x) = 7

4 tan (3 x) = 7

Divide both sides by

4

4 tan (3 x) = 7

Divide both sides by

4

\frac{4 tan ( 3 x )}{4} = \frac{7}{4}

Simplify

tan (3 x) = \frac{7}{4}

tan (3 x) = \frac{7}{4}

Apply trig inverse properties

tan (3 x) = \frac{7}{4}

General solutions for

tan (3 x) = \frac{7}{4}

tan (x) = a \Rightarrow x = arctan (a) + πn

3 x = arctan (\frac{7}{4}) + πn

3 x = arctan (\frac{7}{4}) + πn

Solve

3 x = arctan (\frac{7}{4}) + πn : x = \frac{arctan ( \frac{7}{4} )}{3} + \frac{πn}{3}

3 x = arctan (\frac{7}{4}) + πn

Divide both sides by

3

3 x = arctan (\frac{7}{4}) + πn

Divide both sides by

3

\frac{3 x}{3} = \frac{arctan ( \frac{7}{4} )}{3} + \frac{πn}{3}

Simplify

x = \frac{arctan ( \frac{7}{4} )}{3} + \frac{πn}{3}

x = \frac{arctan ( \frac{7}{4} )}{3} + \frac{πn}{3}

x = \frac{arctan ( \frac{7}{4} )}{3} + \frac{πn}{3}

Show solutions in decimal form

x = \frac{1.05165 \dots}{3} + \frac{πn}{3}

6 sin^{2} (θ) + 13 sin (θ) + 7 = 0

12 sin^{2} (x) - 17 sin (x) + 6 = 0

sin (θ) = \frac{3}{3}

tan (x + π) + cos (x + \frac{π}{2}) = 0

sin (θ) cos (θ) = \frac{3}{4}

What is the general solution for 4sin(3x)=7cos(3x) ?
The general solution for 4sin(3x)=7cos(3x) is x=(1.05165…)/3+(pin)/3